Question

An element has two isotopes of masses of 10.012937 and 11.009305. The first isotope has a percent abundance of 19.8000%. Calculate the atomic mass of the element.

Answer 1

To find the atomic mass of an element with two isotopes, we calculate a weighted average based on the isotopes' masses and percent abundances. With a mass of 10.012937 amu for isotope 1 (with 19.8000% abundance) and 11.009305 amu for isotope 2, the average atomic mass of the element is approximately 10.809 amu.

Step-by-step explanation:

To calculate the atomic mass of an element with two isotopes, we use the formula:

Atomic mass = (% abundance of isotope 1) × (mass of isotope 1) + (% abundance of isotope 2) × (mass of isotope 2)

For the given element with isotopes of masses 10.012937 amu and 11.009305 amu and a percent abundance of 19.8000% for the first isotope, we first convert the percent abundance to decimal form:

• 
  
• %1 = 19.8000% = 0.1980
• 
  
• mass1 = 10.012937 amu

The percent abundance of the second isotope can be calculated as 100% - 19.8000% = 80.2000%, or in decimal form:

• 
  
• %2 = 80.2000% = 0.8020
• 
  
• mass2 = 11.009305 amu

Substituting these into the formula, we get:

Atomic mass = (0.1980 × 10.012937) + (0.8020 × 11.009305)

Performing the calculation:

Atomic mass = (1.982642346) + (8.82646081)

The atomic mass of the element is therefore approximately:

Atomic mass = 1.982642346 + 8.82646081 = 10.809103156 amu

So, the average atomic mass of the element is 10.809 amu.